TDCOSMO V: strategies for precise and accurate measurements of the Hubble constant with strong lensing

TL;DR

The paper addresses the Hubble tension by assessing how precisely $H_0$ can be inferred from strong-lensing time delays without assuming a specific radial mass profile. It adopts a hierarchical framework that jointly models the mass-sheet degeneracy via a population-level MST parameter $\lambda$ and stellar-kinematics anisotropy $a_{ m ani}$, incorporating external datasets when deflectors are drawn from the same population. The key contribution is forecasting that, with current data and technology, $H_0$ can reach $\sim$2–3% precision by adding spatially resolved kinematics and external lenses, and that future samples (40 time-delay + 200 non-time-delay lenses) could achieve $\sim$1.2–1.5%, sufficient to resolve the Hubble tension at $3$–$5\sigma$ without profile assumptions. This approach enables internal consistency checks across samples and paves the way for leveraging upcoming surveys ( Rubin, Euclid, Roman ) to tighten cosmological constraints from time-delay cosmography with minimal model dependence.

Abstract

Strong lensing time delays can measure the Hubble constant H$_0$ independent of any other probe. Assuming commonly used forms for the radial mass density profile of the lenses, a 2\% precision has been achieved with 7 Time-Delay Cosmography (TDCOSMO) lenses, in tension with the H$_0$ from the cosmic microwave background. However, without assumptions on the radial mass density profile -- and relying exclusively on stellar kinematics to break the mass-sheet degeneracy -- the precision drops to 8\% with the current data of the 7 TDCOSMO lenses, insufficient to resolve the H$_0$ tension. With the addition of external information from 33 Sloan Lens ACS (SLACS) lenses, the precision improves to 5\%, {\it if} the deflectors of TDCOSMO and SLACS lenses are drawn from the same population. We investigate the prospects to improve the precision of time-delay cosmography without relying on mass profile assumptions to break the mass sheet degeneracy. Our forecasts are based on the hierarchical framework introduced by Birrer et al. (2020). With existing samples and technology, 3.3\% precision on H$_0$ can be reached by adding spatially resolved kinematics of the 7 TDCOSMO lenses. The precision improves to 2.5\% with the further addition of kinematics for 50 non-time-delay lenses from SLACS and the Strong Lensing Legacy Survey (SL2S). Expanding the samples to 40 time delay and 200 non-time delay lenses will improve the precision to 1.5\% and 1.2\%, respectively. Time-delay cosmography can reach sufficient precision to resolve the Hubble tension at 3-5$σ$, without assumptions on the radial mass profile of lens galaxies. By obtaining this precision with and without external datasets, we will test the consistency of the samples and enable further improvements based on even larger future samples of time delay and non-time-delay lenses (e.g. from the Rubin, Euclid, and Roman Observatories).

Figures (4)

• Figure 1: Forecast precision on H$_0$, the MST parameter $\lambda,$ and the anisotropy parameter $a_{\rm ani}$ for different spectroscopic scenarios of the seven TDCOSMO lenses (current scenario) as specified in Table \ref{['table:param_summary_tdlmc']} column $\delta$H$_0$. https://github.com/sibirrer/TDCOSMO_forecast/blob/master/forecast.ipynb
• Figure 2: Forecast precision on H$_0$, the MST parameter $\lambda,$ and the anisotropy parameter $a_{\rm ani}$ for different spectroscopic scenarios of the seven TDCOSMO lenses (current scenario) observed with aperture spectroscopy of 5% precision as well as in the case where external data sets are added, as specified in Table \ref{['table:param_summary_tdlmc']} (TDCOSMO-5% row). https://github.com/sibirrer/TDCOSMO_forecast/blob/master/forecast.ipynb
• Figure 3: Forecast precision on H$_0$, the MST parameter $\lambda,$ and the anisotropy parameter $a_{\rm ani}$ for different spectroscopic scenarios of a future sample of 40 TDCOSMO lenses (future scenario) as specified in Table \ref{['table:param_summary_tdlmc']} in the row of TDCOSMO-5%. https://github.com/sibirrer/TDCOSMO_forecast/blob/master/forecast.ipynb
• Figure 4: Forecast precision on H$_0$, the MST parameter $\lambda,$ and the anisotropy parameter $a_{\rm ani}$ for different spectroscopic scenarios of a future sample of 40 TDCOSMO lenses (future scenario) observed with aperture spectroscopy of 5% precision and additional external data sets specified in Table \ref{['table:param_summary_tdlmc']} in the row of TDCOSMO-5%. https://github.com/sibirrer/TDCOSMO_forecast/blob/master/forecast.ipynb